期刊
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
卷 19, 期 3, 页码 623-654出版社
SPRINGER
DOI: 10.1007/s10884-006-9013-6
关键词
singular perturbation; Conley index theory; traveling wave; symbolic dynamics; rigorous computation; predator-prey system
We show the existence of a set of periodic traveling waves in a system of two scalar reaction diffusion equations, which is in one-to-one correspondence with a full shift on two symbols. We use a novel combination of rigorous numerical computations and the topological techniques of the Conley index theory. This approach is quite general, and this paper is intended as a demonstration of its usefulness and applicability.
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